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Math Help - Trying to determine equation for mixtures of liquid

  1. #1
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    Trying to determine equation for mixtures of liquid

    The purpose of this is for changing the mixture of a liquid used in electronic cigarettes. I will use an example to describe what I'm asking.


    Current liquid mixture:


    5ml is the total volume of the liquid.


    It has a nicotine strength of 12mg. This means 12mg per ml. That is a total of 60mg of nicotine within the 5ml.


    When mixing the liquid I use a Nicotine base of 37.5mg per ml. The other ingredients used to obtain the total 5ml are unimportant for the scope of this thread.


    Basically it required that 1.6ml of the example nicotine base is part of the 5ml total liquid to acquire 12mg nicotine strength. (60mg divided by 37.5mg)


    WHAT I AM TRYING TO ACHIEVE: I want to up the strength to 18mg of nicotine.


    If I would have made the liquid 18mg to begin with I would have used 2.4ml of nicotine base. Which is a 0.8 increase. Resulting in 18mg strength within 5ml of liquid.


    Of course if add 0.8ml of nicotine base to the already mix liquid I will now have a total of 5.8ml of liquid. This gives me 90mg of liquid, but with now a 5.8ml volume which is only approx 15.5mg of nicotine strenght. I can do the same crude calculations over and over to an X number of times until I get close to 18mg of nicotine strength. When I do it over and over, adjusting more and more, little by little in the math I eventually figure out what I need. Adding somewhere between 1.5 to 1.6ml of my nicotine base results in what I need to add.


    But I want to know if an equation is possible to skip all the trial and error or should I say adjust and then re-adjust.


    I'm not doing all this to help me change one stupid mixture. This would help me accomplish a small but important percentage of what is needed to help a community of e-cigarette users through use of a free software available to them to help them change mixtures when their original mixture doesnt give the result they need. Sometimes they find out after testing their liquid that their nicotine, mixture of ingredients, or flavors are not what they hoped for.


    Variations from the example. Basically I hope for an equation that assumes that: the total volume may not always be 5ml. The intial nicotine strength may not always be 12mg per ml. The target nicotine strength may not always be 18mg per ml. The nicotine base may not always be 37.5mg per ml. Basically there are no constants.


    This is my first post here so I really don't know what to expect from this forum. I appreciate any insight to the conundrum I have.
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  2. #2
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    Re: Trying to determine equation for mixtures of liquid

    No need for trial and error.

    You have 5 mL of liquid with a strength of 12 mg/mL. You are mixing x mL of base with a strength of 37.5 mg/mL and you want to obtain a strength of 18 mg/mL. Since the strength is defined as (nicotine, mg)/(total volume, mL), we compute the amount of nicotine (mg), divided by the total volume (mL).

    \frac{60 + 37.5x}{5 + x} = 18

    60 + 37.5x = 90 + 5x \Rightarrow x = \frac{30}{32.5} \approx 0.923 mL
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    Re: Trying to determine equation for mixtures of liquid

    Quote Originally Posted by richard1234 View Post
    No need for trial and error.

    You have 5 mL of liquid with a strength of 12 mg/mL. You are mixing x mL of base with a strength of 37.5 mg/mL and you want to obtain a strength of 18 mg/mL. Since the strength is defined as (nicotine, mg)/(total volume, mL), we compute the amount of nicotine (mg), divided by the total volume (mL).

    \frac{60 + 37.5x}{5 + x} = 18

    60 + 37.5x = 90 + 5x \Rightarrow x = \frac{30}{32.5} \approx 0.923 mL
    This doesn't work for me. 5mL liquid with 12mg strength nic. 60mg total / by 37.5 is 1.6ml nic based that I originally used. If I add 0.923 to 1.6 I get a total of 2.523ml nic base which is a total of 94.6125mg of nic / 5.923mL only gives me a nic strength of 15.97mg approx.

    Edit: I think your equation works though but I get a different result of 1.53mL approx which works to give me a total of 6.53ml with a strength of 18mg nic. Thanks for your help. This makes life easier.

    I break the equation down to:

    60 + 37.5x = 18(5+x)

    60 + 37.5x = 90 + 18x

    19.5x = 30

    x = 30/19.5

    x = 1.53 approx.
    Last edited by wseyller; June 14th 2012 at 05:46 AM.
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  4. #4
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    Re: Trying to determine equation for mixtures of liquid

    I would assume that the diluent is water containing other ingredients.Is this correct?
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    Re: Trying to determine equation for mixtures of liquid

    The components are Propylene Glycol (PG) and vegetable glycerin (VG). The % of those depends of the persons desire. The nicotine base is diluted with either PG, VG or both. The strength of the base can be up to 100mg per ml which is available to purchase. The other ingredients would be flavorings which are also PG and VG based flavorings. Sometimes a small amount of water or pga could be used to thin out liquid that contain a high % of VG, because VG is very thick.
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  6. #6
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    Re: Trying to determine equation for mixtures of liquid

    To make diluted solutions I assume this is done in bulk like 1000ml of 12mg/ml and another 1000ml of 18mg/.ml and you want to figure the proportions of diluent to stock sol of 37.5 mg/ml

    Example Desired conc 18 mg/ml Nicotine 1000ml* 18 = 18000 mg N Let x = ml of 37.5 mg/ml required x* 37.5 = 18000 x = 480 ml of stock + 520 ml diluent
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  7. #7
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    Re: Trying to determine equation for mixtures of liquid

    Quote Originally Posted by wseyller View Post
    This doesn't work for me. 5mL liquid with 12mg strength nic. 60mg total / by 37.5 is 1.6ml nic based that I originally used. If I add 0.923 to 1.6 I get a total of 2.523ml nic base which is a total of 94.6125mg of nic / 5.923mL only gives me a nic strength of 15.97mg approx.

    Edit: I think your equation works though but I get a different result of 1.53mL approx which works to give me a total of 6.53ml with a strength of 18mg nic. Thanks for your help. This makes life easier.

    I break the equation down to:

    60 + 37.5x = 18(5+x)

    60 + 37.5x = 90 + 18x

    19.5x = 30

    x = 30/19.5

    x = 1.53 approx.
    First off, you can't just add .953 to 1.6. You're adding two different units, mg/mL and mL.

    Whoops, just realized I screwed up a bit too (tried to multiply 18(5+x) in my head, somehow got 90+5x).
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  8. #8
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    Re: Trying to determine equation for mixtures of liquid

    Therefore the correct equation is

    60 + 37.5x = 90 + 18x

    19.5x = 30 \Rightarrow x \approx 1.54 mL
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  9. #9
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    Re: Trying to determine equation for mixtures of liquid

    It would not be in bulk. This is for people, my self included that DIY their own e-liquid. I bought 60mL of Nic (100% PG Based) at 100mg/ml. 100mg is dangerous to handle so I diluted mine to 37.5mg (75%PG/25%VG) with PG and VG to make it safer to handle. Others may have a some other strength or mixture.

    In same cases I may make a juice maybe between 5 to 50ml. I may decide that I want more nicotine or I want to add more flavoring because it isn't strong enough. So I am working on a calculator program that a person inputs specs of what they have, then input what the target is. Then have the program calculate the minimum ingredients required to reach the target.

    I used to be good at math but that was 15 years ago when I took trig and stuff in college. I forgot most of it.

    It will be a good challenge for me. I'm working on getting good equations to handle all of this and rely less on logic and loops which i a kind of dirty way of doing it. This one equation should give me a good step into completing my goal. The hard part is that everything changes everything else. Adding flavors, VG or, PG dilutes the nic. Adding nic dilutes the flavor. Flavoring and nic added may change the desired PG/VG ratio. It allow us to save the juice and not have to waste it and start all over.
    Last edited by wseyller; June 14th 2012 at 09:20 AM.
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